Geodesic
On coset-spaces of compact Lie groups by subgrops of corank two
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 68-77.

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Let $G$ and $G'$ be compact connected simply connected Lie groups. Suppose that $G$ is a simple group, $L$ is a centralizer of torus of $G$, $H$ is the commutant of the subgroup $L$, and $\mathrm{rk}~G - \mathrm{rk}~H = 2$. Let $\mathrm{Sam}~(G/H) = 0$. We prove the following assertion: if the group $G'$ acts transitively and almost effectively on the manifold $G/H$, then $G' \cong G$. If all lenghts of roots of the group $G$ are equal, then the action of $G'$ on $G/H$ is similar to the action of $G$.
Mots-clés : compact Lie group
Keywords: cohomology, homotopy groups, transitive action. 
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     title = {On coset-spaces of compact {Lie} groups by subgrops of corank two},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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     number = {11},
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A. N. Shchetinin. On coset-spaces of compact Lie groups by subgrops of corank two. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 68-77. http://geodesic.mathdoc.fr/item/IVM_2017_11_a7/

[1] Schetinin A. N., “O faktor-prostranstvakh kompaktnykh grupp Li po podgruppam koranga edinitsa”, Izv. vuzov. Matem., 2015, no. 6, 60–74

[2] Onischik A. L., Topologiya tranzitivnykh grupp preobrazovanii, Fizmatlit, M., 1995

[3] Burbaki N., Gruppy i algebry Li. Gl. IV–VI, Mir, M., 1972

[4] Rokhlin V. A., Fuks D. B., Nachalnyi kurs topologii, Nauka, M., 1977

[5] Bott R., Samelson H., “Applications of the theory of Morse to symmetric spaces”, Amer. J. Math., 80:4 (1958), 964–1029 | DOI | MR

[6] Kervaire M. A., “Some nonstable homotopy groups of Lie groups”, Ill. J. Math., 4:2 (1960), 161–169 | MR | Zbl

[7] Toda H., “Quelques tables des groupes d'homotopie des groupes de Lie”, C. R. Acad. Sci. Paris, 241:5 (1955), 922–923 | MR | Zbl

[8] Imanishi H., “Unstable homotopy groups of classsical Lie groups (odd primary components)”, J. Math. Kyoto Univ., 7:3 (1967), 221–243 | DOI | MR | Zbl

[9] Dynkin E. B., Onischik A. L., “Kompaktnye gruppy Li v tselom”, UMN, 10:4 (1955), 3–74 | Zbl

[10] Schetinin A. N., “O rangakh gomotopicheskikh grupp odnorodnykh prostranstv”, Matem. zametki, 86:6 (2009), 912–924 | DOI | Zbl

[11] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Matem. sb., 30:2 (1952), 349–462 | Zbl

[12] Onischik A. L., “O topologii nekotorykh kompleksnykh odnorodnykh prostranstv”, Mnogomern. kompl. analiz, In-t fiziki SO AN SSR, Krasnoyarsk, 1985, 109–121

[13] Dynkin E. B., “Maksimalnye podalgebry poluprostykh algebr Li”, Trudy MMO, 1, 1952, 39–166 | Zbl

[14] Mkhitaryan V. G., “Podalgebry koranga $1$ v kompaktnykh algebrakh Li”, Vopr. teorii grupp i gomolog. algebry, Yaroslavskii un-t, Yaroslavl, 1982, 119–126